Data 621 Homework #4:
Overview
In this homework assignment, you will explore, analyze and model a data set containing approximately 8000 records representing a customer at an auto insurance company. Each record has two response variables. The first response variable, TARGET_FLAG, is a 1 or a 0. A "“1” means that the person was in a car crash. A zero means that the person was not in a car crash. The second response variable is TARGET_AMT. This value is zero if the person did not crash their car. But if they did crash their car, this number will be a value greater than zero.
Your objective is to build multiple linear regression and binary logistic regression models on the training data to predict the probability that a person will crash their car and also the amount of money it will cost if the person does crash their car. You can only use the variables given to you (or variables that you derive from the variables provided).
Data Exploration and Data Preparation
The first step we did was to import the data from GitHub, remove the index and look at the structure of the data.
train <- read.csv("https://raw.githubusercontent.com/destination4debabrata/CUNY-Assignments/master/DATA%20621%2001%5B46893%5D/Week%2010%20Weighted%20Least%20Squares%20and%20Robust%20Regression%20%5BMar%2030%20-%20Apr%2005%5D/insurance_training_data.csv", stringsAsFactors = TRUE)
eval <- read.csv("https://raw.githubusercontent.com/destination4debabrata/CUNY-Assignments/master/DATA%20621%2001%5B46893%5D/Week%2010%20Weighted%20Least%20Squares%20and%20Robust%20Regression%20%5BMar%2030%20-%20Apr%2005%5D/insurance-evaluation-data.csv",stringsAsFactors = TRUE)
train <- train[-c(1)] # remove index column
eval <- eval[-c(1)]
str(train)## 'data.frame': 8161 obs. of 25 variables:
## $ TARGET_FLAG: int 0 0 0 0 0 1 0 1 1 0 ...
## $ TARGET_AMT : num 0 0 0 0 0 ...
## $ KIDSDRIV : int 0 0 0 0 0 0 0 1 0 0 ...
## $ AGE : int 60 43 35 51 50 34 54 37 34 50 ...
## $ HOMEKIDS : int 0 0 1 0 0 1 0 2 0 0 ...
## $ YOJ : int 11 11 10 14 NA 12 NA NA 10 7 ...
## $ INCOME : Factor w/ 6613 levels "","$0","$1,007",..: 5033 6292 1250 1 509 746 1488 315 4765 282 ...
## $ PARENT1 : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 2 1 1 1 1 ...
## $ HOME_VAL : Factor w/ 5107 levels "","$0","$100,093",..: 2 3259 348 3917 3034 2 1 4167 2 2 ...
## $ MSTATUS : Factor w/ 2 levels "Yes","z_No": 2 2 1 1 1 2 1 1 2 2 ...
## $ SEX : Factor w/ 2 levels "M","z_F": 1 1 2 1 2 2 2 1 2 1 ...
## $ EDUCATION : Factor w/ 5 levels "<High School",..: 4 5 5 1 4 2 1 2 2 2 ...
## $ JOB : Factor w/ 9 levels "","Clerical",..: 7 9 2 9 3 9 9 9 2 7 ...
## $ TRAVTIME : int 14 22 5 32 36 46 33 44 34 48 ...
## $ CAR_USE : Factor w/ 2 levels "Commercial","Private": 2 1 2 2 2 1 2 1 2 1 ...
## $ BLUEBOOK : Factor w/ 2789 levels "$1,500","$1,520",..: 434 503 2212 553 802 746 2672 701 135 852 ...
## $ TIF : int 11 1 4 7 1 1 1 1 1 7 ...
## $ CAR_TYPE : Factor w/ 6 levels "Minivan","Panel Truck",..: 1 1 6 1 6 4 6 5 6 5 ...
## $ RED_CAR : Factor w/ 2 levels "no","yes": 2 2 1 2 1 1 1 2 1 1 ...
## $ OLDCLAIM : Factor w/ 2857 levels "$0","$1,000",..: 1449 1 1311 1 432 1 1 510 1 1 ...
## $ CLM_FREQ : int 2 0 2 0 2 0 0 1 0 0 ...
## $ REVOKED : Factor w/ 2 levels "No","Yes": 1 1 1 1 2 1 1 2 1 1 ...
## $ MVR_PTS : int 3 0 3 0 3 0 0 10 0 1 ...
## $ CAR_AGE : int 18 1 10 6 17 7 1 7 1 17 ...
## $ URBANICITY : Factor w/ 2 levels "Highly Urban/ Urban",..: 1 1 1 1 1 1 1 1 1 2 ...We removed special characters then converted variables to numbers for both the Training and Evaluation data.
train$INCOME<-gsub("[\\$,]", "", train$INCOME)
train$HOME_VAL<-gsub("[\\$,]", "", train$HOME_VAL)
train$BLUEBOOK<-gsub("[\\$,]", "", train$BLUEBOOK)
train$OLDCLAIM<-gsub("[\\$,]", "",train$OLDCLAIM)
eval$INCOME<-gsub("[\\$,]", "", eval$INCOME)
eval$HOME_VAL<-gsub("[\\$,]", "", eval$HOME_VAL)
eval$BLUEBOOK<-gsub("[\\$,]", "", eval$BLUEBOOK)
eval$OLDCLAIM<-gsub("[\\$,]", "",eval$OLDCLAIM)
train$INCOME<-as.numeric(train$INCOME)
train$HOME_VAL<-as.numeric(train$HOME_VAL)
train$BLUEBOOK<-as.numeric(train$BLUEBOOK)
train$OLDCLAIM<-as.numeric(train$OLDCLAIM)
eval$INCOME<-as.numeric(eval$INCOME)
eval$HOME_VAL<-as.numeric(eval$HOME_VAL)
eval$BLUEBOOK<-as.numeric(eval$BLUEBOOK)
eval$OLDCLAIM<-as.numeric(eval$OLDCLAIM)We then split the training data into a train and test data set.
set.seed(123)
sample <- sample.split(train,SplitRatio = 0.80)
train <- subset(train, sample == TRUE)
test <- subset(train, sample == FALSE)## TARGET_FLAG TARGET_AMT KIDSDRIV AGE
## Min. :0.000 Min. : 0 Min. :0.0000 Min. :16.00
## 1st Qu.:0.000 1st Qu.: 0 1st Qu.:0.0000 1st Qu.:39.00
## Median :0.000 Median : 0 Median :0.0000 Median :45.00
## Mean :0.265 Mean : 1491 Mean :0.1731 Mean :44.85
## 3rd Qu.:1.000 3rd Qu.: 1102 3rd Qu.:0.0000 3rd Qu.:51.00
## Max. :1.000 Max. :85524 Max. :4.0000 Max. :76.00
## NA's :6
## HOMEKIDS YOJ INCOME PARENT1 HOME_VAL
## Min. :0.0000 Min. : 0.00 Min. : 0 No :5663 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 9.00 1st Qu.: 27646 Yes: 866 1st Qu.: 0
## Median :0.0000 Median :11.00 Median : 54005 Median :160945
## Mean :0.7265 Mean :10.49 Mean : 61552 Mean :154188
## 3rd Qu.:1.0000 3rd Qu.:13.00 3rd Qu.: 85697 3rd Qu.:238750
## Max. :5.0000 Max. :19.00 Max. :367030 Max. :885282
## NA's :370 NA's :350 NA's :358
## MSTATUS SEX EDUCATION JOB
## Yes :3936 M :3033 <High School : 971 z_Blue Collar:1476
## z_No:2593 z_F:3496 Bachelors :1798 Clerical : 997
## Masters :1324 Professional : 901
## PhD : 577 Manager : 783
## z_High School:1859 Lawyer : 665
## Student : 573
## (Other) :1134
## TRAVTIME CAR_USE BLUEBOOK TIF
## Min. : 5.00 Commercial:2440 Min. : 1500 Min. : 1.000
## 1st Qu.: 23.00 Private :4089 1st Qu.: 9260 1st Qu.: 1.000
## Median : 33.00 Median :14440 Median : 4.000
## Mean : 33.58 Mean :15684 Mean : 5.357
## 3rd Qu.: 44.00 3rd Qu.:20800 3rd Qu.: 7.000
## Max. :142.00 Max. :65970 Max. :25.000
##
## CAR_TYPE RED_CAR OLDCLAIM CLM_FREQ REVOKED
## Minivan :1706 no :4623 Min. : 0 Min. :0.0000 No :5742
## Panel Truck: 550 yes:1906 1st Qu.: 0 1st Qu.:0.0000 Yes: 787
## Pickup :1083 Median : 0 Median :0.0000
## Sports Car : 732 Mean : 3982 Mean :0.7961
## Van : 612 3rd Qu.: 4633 3rd Qu.:2.0000
## z_SUV :1846 Max. :57037 Max. :5.0000
##
## MVR_PTS CAR_AGE URBANICITY
## Min. : 0.000 Min. : 0.000 Highly Urban/ Urban :5169
## 1st Qu.: 0.000 1st Qu.: 1.000 z_Highly Rural/ Rural:1360
## Median : 1.000 Median : 8.000
## Mean : 1.695 Mean : 8.255
## 3rd Qu.: 3.000 3rd Qu.:12.000
## Max. :13.000 Max. :28.000
## NA's :415## variable q_zeros p_zeros q_na p_na q_inf p_inf type unique
## 1 TARGET_FLAG 4799 73.50 0 0.00 0 0 integer 2
## 2 TARGET_AMT 4799 73.50 0 0.00 0 0 numeric 1595
## 3 KIDSDRIV 5735 87.84 0 0.00 0 0 integer 5
## 4 AGE 0 0.00 6 0.09 0 0 integer 57
## 5 HOMEKIDS 4219 64.62 0 0.00 0 0 integer 6
## 6 YOJ 512 7.84 370 5.67 0 0 integer 20
## 7 INCOME 507 7.77 350 5.36 0 0 numeric 5347
## 8 PARENT1 0 0.00 0 0.00 0 0 factor 2
## 9 HOME_VAL 1852 28.37 358 5.48 0 0 numeric 4121
## 10 MSTATUS 0 0.00 0 0.00 0 0 factor 2
## 11 SEX 0 0.00 0 0.00 0 0 factor 2
## 12 EDUCATION 0 0.00 0 0.00 0 0 factor 5
## 13 JOB 0 0.00 0 0.00 0 0 factor 9
## 14 TRAVTIME 0 0.00 0 0.00 0 0 integer 95
## 15 CAR_USE 0 0.00 0 0.00 0 0 factor 2
## 16 BLUEBOOK 0 0.00 0 0.00 0 0 numeric 2572
## 17 TIF 0 0.00 0 0.00 0 0 integer 23
## 18 CAR_TYPE 0 0.00 0 0.00 0 0 factor 6
## 19 RED_CAR 0 0.00 0 0.00 0 0 factor 2
## 20 OLDCLAIM 4006 61.36 0 0.00 0 0 numeric 2336
## 21 CLM_FREQ 4006 61.36 0 0.00 0 0 integer 6
## 22 REVOKED 0 0.00 0 0.00 0 0 factor 2
## 23 MVR_PTS 2967 45.44 0 0.00 0 0 integer 13
## 24 CAR_AGE 2 0.03 415 6.36 0 0 integer 28
## 25 URBANICITY 0 0.00 0 0.00 0 0 factor 2## [1] "TARGET_FLAG" "TARGET_AMT" "KIDSDRIV" "HOMEKIDS" "OLDCLAIM"
## [6] "CLM_FREQ"train2 <- dplyr::select(train, -c(KIDSDRIV,HOMEKIDS,OLDCLAIM,CLM_FREQ))
test <- dplyr::select(test, -c(KIDSDRIV,HOMEKIDS,OLDCLAIM,CLM_FREQ))## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## PARENT1 frequency percentage cumulative_perc
## 1 No 5663 86.74 86.74
## 2 Yes 866 13.26 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## MSTATUS frequency percentage cumulative_perc
## 1 Yes 3936 60.28 60.28
## 2 z_No 2593 39.72 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## SEX frequency percentage cumulative_perc
## 1 z_F 3496 53.55 53.55
## 2 M 3033 46.45 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## EDUCATION frequency percentage cumulative_perc
## 1 z_High School 1859 28.47 28.47
## 2 Bachelors 1798 27.54 56.01
## 3 Masters 1324 20.28 76.29
## 4 <High School 971 14.87 91.16
## 5 PhD 577 8.84 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## JOB frequency percentage cumulative_perc
## 1 z_Blue Collar 1476 22.61 22.61
## 2 Clerical 997 15.27 37.88
## 3 Professional 901 13.80 51.68
## 4 Manager 783 11.99 63.67
## 5 Lawyer 665 10.19 73.86
## 6 Student 573 8.78 82.64
## 7 Home Maker 517 7.92 90.56
## 8 419 6.42 96.98
## 9 Doctor 198 3.03 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## CAR_USE frequency percentage cumulative_perc
## 1 Private 4089 62.63 62.63
## 2 Commercial 2440 37.37 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## CAR_TYPE frequency percentage cumulative_perc
## 1 z_SUV 1846 28.27 28.27
## 2 Minivan 1706 26.13 54.40
## 3 Pickup 1083 16.59 70.99
## 4 Sports Car 732 11.21 82.20
## 5 Van 612 9.37 91.57
## 6 Panel Truck 550 8.42 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## RED_CAR frequency percentage cumulative_perc
## 1 no 4623 70.81 70.81
## 2 yes 1906 29.19 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## REVOKED frequency percentage cumulative_perc
## 1 No 5742 87.95 87.95
## 2 Yes 787 12.05 100.00## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.## Warning: Use of `tbl_plot$frequency` is discouraged. Use `frequency` instead.## Warning: Use of `tbl_plot$category` is discouraged. Use `category` instead.
## URBANICITY frequency percentage cumulative_perc
## 1 Highly Urban/ Urban 5169 79.17 79.17
## 2 z_Highly Rural/ Rural 1360 20.83 100.00## [1] "Variables processed: PARENT1, MSTATUS, SEX, EDUCATION, JOB, CAR_USE, CAR_TYPE, RED_CAR, REVOKED, URBANICITY"We can determine the skewness and kurtosis of the data.
Impute values
The missing NA values were imputed with the median using the Hmisc package:
train2$AGE<-impute(train2$AGE, median)
train2$YOJ<-impute(train2$YOJ, median)
train2$INCOME<-impute(train2$INCOME, median)
train2$CAR_AGE<-impute(train2$CAR_AGE, median)
eval$AGE<-impute(eval$AGE, median)
eval$YOJ<-impute(eval$YOJ, median)
eval$INCOME<-impute(eval$INCOME, median)
eval$CAR_AGE<-impute(eval$CAR_AGE, median)Create new variable
We created new variable which is PTSAGE = MVR_PTS/AGE.
Build Models
Predicting car crash
In the model, we selected the following variables.
model1 = glm(TARGET_FLAG ~ YOJ + INCOME + PARENT1 + HOME_VAL + MSTATUS + SEX + EDUCATION + JOB + TRAVTIME + CAR_USE + TIF + CAR_TYPE + RED_CAR + REVOKED + URBANICITY + PTSAGE,data = train2, family = 'binomial')
summary(model1)##
## Call:
## glm(formula = TARGET_FLAG ~ YOJ + INCOME + PARENT1 + HOME_VAL +
## MSTATUS + SEX + EDUCATION + JOB + TRAVTIME + CAR_USE + TIF +
## CAR_TYPE + RED_CAR + REVOKED + URBANICITY + PTSAGE, family = "binomial",
## data = train2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1603 -0.7234 -0.4181 0.6649 3.0602
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -1.154e+00 3.097e-01 -3.727 0.000194 ***
## YOJ -6.191e-03 9.490e-03 -0.652 0.514169
## INCOME -2.730e-06 1.238e-06 -2.204 0.027514 *
## PARENT1Yes 5.639e-01 1.047e-01 5.383 7.32e-08 ***
## HOME_VAL -1.351e-06 3.913e-07 -3.454 0.000553 ***
## MSTATUSz_No 3.830e-01 9.266e-02 4.133 3.58e-05 ***
## SEXz_F -2.449e-01 1.175e-01 -2.085 0.037062 *
## EDUCATIONBachelors -3.601e-01 1.244e-01 -2.896 0.003784 **
## EDUCATIONMasters -3.924e-01 1.868e-01 -2.101 0.035649 *
## EDUCATIONPhD -1.700e-01 2.270e-01 -0.749 0.453831
## EDUCATIONz_High School 7.008e-02 1.083e-01 0.647 0.517416
## JOBClerical 4.164e-01 2.240e-01 1.859 0.063050 .
## JOBDoctor -6.475e-01 3.043e-01 -2.128 0.033362 *
## JOBHome Maker 2.450e-01 2.379e-01 1.030 0.303225
## JOBLawyer 9.244e-02 1.911e-01 0.484 0.628575
## JOBManager -6.692e-01 1.978e-01 -3.383 0.000717 ***
## JOBProfessional 8.490e-02 2.034e-01 0.417 0.676417
## JOBStudent 3.574e-01 2.444e-01 1.462 0.143642
## JOBz_Blue Collar 2.867e-01 2.122e-01 1.351 0.176615
## TRAVTIME 1.593e-02 2.122e-03 7.509 5.94e-14 ***
## CAR_USEPrivate -6.998e-01 1.050e-01 -6.665 2.64e-11 ***
## TIF -5.058e-02 8.294e-03 -6.099 1.07e-09 ***
## CAR_TYPEPanel Truck 3.056e-01 1.613e-01 1.895 0.058144 .
## CAR_TYPEPickup 5.584e-01 1.151e-01 4.853 1.22e-06 ***
## CAR_TYPESports Car 1.199e+00 1.374e-01 8.724 < 2e-16 ***
## CAR_TYPEVan 4.925e-01 1.393e-01 3.536 0.000407 ***
## CAR_TYPEz_SUV 9.610e-01 1.162e-01 8.272 < 2e-16 ***
## RED_CARyes -5.146e-02 9.856e-02 -0.522 0.601606
## REVOKEDYes 7.648e-01 9.198e-02 8.315 < 2e-16 ***
## URBANICITYz_Highly Rural/ Rural -2.436e+00 1.255e-01 -19.415 < 2e-16 ***
## PTSAGE 5.356e+00 5.792e-01 9.247 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 7129.6 on 6170 degrees of freedom
## Residual deviance: 5609.8 on 6140 degrees of freedom
## (358 observations deleted due to missingness)
## AIC: 5671.8
##
## Number of Fisher Scoring iterations: 5However we removed variables that deemed insufficient.
model2 = glm(TARGET_FLAG ~ INCOME + PARENT1 + HOME_VAL + MSTATUS + EDUCATION + TRAVTIME + CAR_USE + TIF + CAR_TYPE + REVOKED + URBANICITY + PTSAGE, data = train2, family = 'binomial')
summary(model2)##
## Call:
## glm(formula = TARGET_FLAG ~ INCOME + PARENT1 + HOME_VAL + MSTATUS +
## EDUCATION + TRAVTIME + CAR_USE + TIF + CAR_TYPE + REVOKED +
## URBANICITY + PTSAGE, family = "binomial", data = train2)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.1696 -0.7337 -0.4349 0.6606 3.0671
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -8.296e-01 1.684e-01 -4.928 8.31e-07 ***
## INCOME -4.457e-06 1.120e-06 -3.981 6.87e-05 ***
## PARENT1Yes 5.555e-01 1.031e-01 5.385 7.22e-08 ***
## HOME_VAL -1.425e-06 3.774e-07 -3.775 0.000160 ***
## MSTATUSz_No 3.718e-01 9.037e-02 4.115 3.88e-05 ***
## EDUCATIONBachelors -5.966e-01 1.115e-01 -5.352 8.68e-08 ***
## EDUCATIONMasters -6.731e-01 1.251e-01 -5.380 7.44e-08 ***
## EDUCATIONPhD -6.456e-01 1.665e-01 -3.877 0.000106 ***
## EDUCATIONz_High School -4.559e-02 1.044e-01 -0.437 0.662453
## TRAVTIME 1.646e-02 2.102e-03 7.827 4.99e-15 ***
## CAR_USEPrivate -8.303e-01 8.391e-02 -9.895 < 2e-16 ***
## TIF -4.973e-02 8.240e-03 -6.035 1.59e-09 ***
## CAR_TYPEPanel Truck 2.685e-01 1.481e-01 1.813 0.069811 .
## CAR_TYPEPickup 5.028e-01 1.118e-01 4.496 6.93e-06 ***
## CAR_TYPESports Car 1.044e+00 1.186e-01 8.808 < 2e-16 ***
## CAR_TYPEVan 4.819e-01 1.342e-01 3.590 0.000330 ***
## CAR_TYPEz_SUV 8.294e-01 9.490e-02 8.739 < 2e-16 ***
## REVOKEDYes 7.795e-01 9.108e-02 8.559 < 2e-16 ***
## URBANICITYz_Highly Rural/ Rural -2.360e+00 1.250e-01 -18.875 < 2e-16 ***
## PTSAGE 5.541e+00 5.745e-01 9.645 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 7129.6 on 6170 degrees of freedom
## Residual deviance: 5677.2 on 6151 degrees of freedom
## (358 observations deleted due to missingness)
## AIC: 5717.2
##
## Number of Fisher Scoring iterations: 5After removing the unecessary variables, all coefficients fall in line with their theoretical effects.
The model has a majority of the variables with significant p-values, with the exception of 2 categories of education (high school) and car type (truck). All of the coefficients of the variables also fall in line with theoretical effects.
Amount Predicted
train2_claims = train2 %>% filter(TARGET_FLAG == 1)
test_claims = test %>% filter(TARGET_FLAG == 1)
linearmodel1 = lm(TARGET_AMT ~ .-TARGET_FLAG, data = train2_claims)
summary(linearmodel1)##
## Call:
## lm(formula = TARGET_AMT ~ . - TARGET_FLAG, data = train2_claims)
##
## Residuals:
## Min 1Q Median 3Q Max
## -8473 -3015 -1393 568 76295
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.085e+03 1.773e+03 1.741 0.081949 .
## YOJ 4.300e+01 5.164e+01 0.833 0.405148
## INCOME -4.142e-03 7.301e-03 -0.567 0.570612
## PARENT1Yes -3.944e+02 5.176e+02 -0.762 0.446170
## HOME_VAL 1.232e-03 2.192e-03 0.562 0.574090
## MSTATUSz_No 1.161e+03 5.091e+02 2.281 0.022660 *
## SEXz_F -1.011e+03 7.043e+02 -1.436 0.151154
## EDUCATIONBachelors 8.035e+01 6.935e+02 0.116 0.907772
## EDUCATIONMasters 1.442e+03 1.182e+03 1.220 0.222527
## EDUCATIONPhD 1.492e+03 1.393e+03 1.071 0.284439
## EDUCATIONz_High School -7.167e+02 5.571e+02 -1.287 0.198413
## JOBClerical 6.019e+02 1.300e+03 0.463 0.643432
## JOBDoctor -1.132e+03 1.927e+03 -0.587 0.557010
## JOBHome Maker 1.299e+03 1.359e+03 0.956 0.339060
## JOBLawyer 9.975e+02 1.103e+03 0.904 0.366077
## JOBManager -1.581e+02 1.193e+03 -0.133 0.894599
## JOBProfessional 2.152e+03 1.219e+03 1.766 0.077621 .
## JOBStudent 1.523e+03 1.385e+03 1.099 0.271811
## JOBz_Blue Collar 1.619e+03 1.241e+03 1.304 0.192348
## TRAVTIME -2.845e+00 1.181e+01 -0.241 0.809624
## CAR_USEPrivate -1.720e+02 5.619e+02 -0.306 0.759581
## BLUEBOOK 1.186e-01 3.280e-02 3.617 0.000308 ***
## TIF 3.672e+00 4.486e+01 0.082 0.934772
## CAR_TYPEPanel Truck -5.591e+02 1.028e+03 -0.544 0.586808
## CAR_TYPEPickup 1.181e+01 6.455e+02 0.018 0.985405
## CAR_TYPESports Car 1.345e+03 7.953e+02 1.691 0.091001 .
## CAR_TYPEVan -4.801e+02 8.319e+02 -0.577 0.563937
## CAR_TYPEz_SUV 8.016e+02 7.101e+02 1.129 0.259130
## RED_CARyes -1.670e+01 5.347e+02 -0.031 0.975087
## REVOKEDYes -9.291e+02 4.458e+02 -2.084 0.037277 *
## CAR_AGE -1.147e+02 4.753e+01 -2.414 0.015877 *
## URBANICITYz_Highly Rural/ Rural -5.489e+02 8.108e+02 -0.677 0.498498
## PTSAGE 2.351e+03 2.599e+03 0.904 0.365915
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7210 on 1599 degrees of freedom
## (98 observations deleted due to missingness)
## Multiple R-squared: 0.03284, Adjusted R-squared: 0.01349
## F-statistic: 1.697 on 32 and 1599 DF, p-value: 0.009073A lot of the variables are insignificant so we will limit the variables in the next model to make it more significant.
linearmodel2 = lm(TARGET_AMT ~ MSTATUS + BLUEBOOK + CAR_AGE, data = train2_claims)
summary(linearmodel2)##
## Call:
## lm(formula = TARGET_AMT ~ MSTATUS + BLUEBOOK + CAR_AGE, data = train2_claims)
##
## Residuals:
## Min 1Q Median 3Q Max
## -7721 -3027 -1490 351 78332
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4339.86307 423.06857 10.258 < 2e-16 ***
## MSTATUSz_No 754.61699 347.16539 2.174 0.0299 *
## BLUEBOOK 0.09451 0.02106 4.487 7.68e-06 ***
## CAR_AGE -60.72690 33.03295 -1.838 0.0662 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7200 on 1726 degrees of freedom
## Multiple R-squared: 0.01471, Adjusted R-squared: 0.013
## F-statistic: 8.591 on 3 and 1726 DF, p-value: 1.163e-05The coefficients are in line with theoretical effects in this model.
Select Model
Linear Models
## TARGET_FLAG TARGET_AMT YOJ INCOME PARENT1
## Min. :1 Min. : 159.2 Min. : 0.00 Min. : 0 No :275
## 1st Qu.:1 1st Qu.: 2632.2 1st Qu.: 9.00 1st Qu.: 17853 Yes: 81
## Median :1 Median : 4159.5 Median :11.00 Median : 41299
## Mean :1 Mean : 5616.0 Mean :10.08 Mean : 49377
## 3rd Qu.:1 3rd Qu.: 5727.7 3rd Qu.:13.00 3rd Qu.: 70128
## Max. :1 Max. :60838.1 Max. :19.00 Max. :320127
## NA's :24 NA's :16
## HOME_VAL MSTATUS SEX EDUCATION JOB
## Min. : 0 Yes :172 M :162 <High School : 58 z_Blue Collar:97
## 1st Qu.: 0 z_No:184 z_F:194 Bachelors : 84 Clerical :66
## Median :101563 Masters : 55 Student :46
## Mean :108545 PhD : 18 Home Maker :37
## 3rd Qu.:190761 z_High School:141 Professional :36
## Max. :750455 :25
## NA's :18 (Other) :49
## TRAVTIME CAR_USE BLUEBOOK TIF
## Min. : 5.00 Commercial:178 Min. : 1500 Min. : 1.000
## 1st Qu.:24.00 Private :178 1st Qu.: 7338 1st Qu.: 1.000
## Median :35.00 Median :12245 Median : 4.000
## Mean :35.17 Mean :14643 Mean : 4.747
## 3rd Qu.:46.00 3rd Qu.:20215 3rd Qu.: 7.000
## Max. :81.00 Max. :62240 Max. :18.000
##
## CAR_TYPE RED_CAR REVOKED CAR_AGE
## Minivan : 65 no :254 No :297 Min. : 1.000
## Panel Truck: 35 yes:102 Yes: 59 1st Qu.: 1.000
## Pickup : 76 Median : 7.000
## Sports Car : 49 Mean : 7.061
## Van : 29 3rd Qu.:10.750
## z_SUV :102 Max. :22.000
## NA's :30
## URBANICITY PTSAGE
## Highly Urban/ Urban :343 Min. :0.00000
## z_Highly Rural/ Rural: 13 1st Qu.:0.00000
## Median :0.04651
## Mean :0.06580
## 3rd Qu.:0.10217
## Max. :0.42308
## ## [,1]
## [1,] 45889850
## [2,] 47757957
## [3,] 47757957Logit Models
## fitting null model for pseudo-r2## llh llhNull G2 McFadden r2ML
## -2804.9002913 -3564.8219813 1519.8433799 0.2131724 0.2183030
## r2CU
## 0.3186664## fitting null model for pseudo-r2## llh llhNull G2 McFadden r2ML
## -2838.6188224 -3564.8219813 1452.4063178 0.2037137 0.2097137
## r2CU
## 0.3061283fitted.results = predict(model2, test, type = 'response')
fitted.results = ifelse(fitted.results > 0.5, 1, 0)
misClasificError = mean(fitted.results != test$TARGET_FLAG, na.rm = TRUE)
print(paste('Accurancy', round(1-misClasificError, 3)))## [1] "Accurancy 0.784"##
## 1 values imputed to 45
##
##
## 94 values imputed to 11
##
##
## 125 values imputed to 51778
##
##
## 129 values imputed to 8
##
##
## 1 values imputed to 0.02222222## TARGET_FLAG TARGET_AMT KIDSDRIV AGE
## Mode:logical Mode:logical Min. :0.0000 Min. :17.00
## NA's:2141 NA's:2141 1st Qu.:0.0000 1st Qu.:39.00
## Median :0.0000 Median :45.00
## Mean :0.1625 Mean :45.02
## 3rd Qu.:0.0000 3rd Qu.:51.00
## Max. :3.0000 Max. :73.00
##
## HOMEKIDS YOJ INCOME PARENT1 HOME_VAL
## Min. :0.0000 Min. : 0.00 Min. : 0 No :1875 Min. : 0
## 1st Qu.:0.0000 1st Qu.: 9.00 1st Qu.: 27450 Yes: 266 1st Qu.: 0
## Median :0.0000 Median :11.00 Median : 51778 Median :158840
## Mean :0.7174 Mean :10.41 Mean : 59825 Mean :153218
## 3rd Qu.:1.0000 3rd Qu.:13.00 3rd Qu.: 82918 3rd Qu.:236652
## Max. :5.0000 Max. :19.00 Max. :291182 Max. :669271
## NA's :111
## MSTATUS SEX EDUCATION JOB
## Yes :1294 M : 971 <High School :312 z_Blue Collar:463
## z_No: 847 z_F:1170 Bachelors :581 Clerical :319
## Masters :420 Professional :291
## PhD :206 Manager :269
## z_High School:622 Home Maker :202
## Lawyer :196
## (Other) :401
## TRAVTIME CAR_USE BLUEBOOK TIF
## Min. : 5.00 Commercial: 760 Min. : 1500 Min. : 1.000
## 1st Qu.: 22.00 Private :1381 1st Qu.: 8870 1st Qu.: 1.000
## Median : 33.00 Median :14170 Median : 4.000
## Mean : 33.15 Mean :15469 Mean : 5.245
## 3rd Qu.: 43.00 3rd Qu.:21050 3rd Qu.: 7.000
## Max. :105.00 Max. :49940 Max. :25.000
##
## CAR_TYPE RED_CAR OLDCLAIM CLM_FREQ REVOKED
## Minivan :549 no :1543 Min. : 0 Min. :0.000 No :1880
## Panel Truck:177 yes: 598 1st Qu.: 0 1st Qu.:0.000 Yes: 261
## Pickup :383 Median : 0 Median :0.000
## Sports Car :272 Mean : 4022 Mean :0.809
## Van :171 3rd Qu.: 4718 3rd Qu.:2.000
## z_SUV :589 Max. :54399 Max. :5.000
##
## MVR_PTS CAR_AGE URBANICITY
## Min. : 0.000 Min. : 0.000 Highly Urban/ Urban :1738
## 1st Qu.: 0.000 1st Qu.: 1.000 z_Highly Rural/ Rural: 403
## Median : 1.000 Median : 8.000
## Mean : 1.766 Mean : 8.172
## 3rd Qu.: 3.000 3rd Qu.:12.000
## Max. :12.000 Max. :26.000
##
## PTSAGE
## Min. :0.00000
## 1st Qu.:0.00000
## Median :0.02128
## Mean :0.04227
## 3rd Qu.:0.06522
## Max. :0.50000
##